As an internal combustion engine in which the air fuel ratio of an air-fuel mixture can be changed, there has been known one in which an exhaust gas purification device including an NSR catalyst is arranged in an exhaust passage. In such an internal combustion engine, there has been proposed a technology in which at the time when an amount of NOx stored in the NSR catalyst (a storage amount of NOx) becomes equal to or more than a predetermined threshold value when the air fuel ratio of the air-fuel mixture is a lean air fuel ratio which is an air fuel ratio higher than a stoichiometric air fuel ratio, the air fuel ratio of exhaust gas flowing into the NSR catalyst is controlled from the stoichiometric air fuel ratio to a rich air fuel ratio (rich spike processing), so that the NOx stored in the NSR catalyst is reduced and purified (removed). In addition, there has also been proposed a technology in which when the storage amount of NOx in the NSR catalyst is more than a predetermined amount which is smaller than the above-mentioned predetermined threshold value at the time when the air fuel ratio of the air-fuel mixture is changed from a lean air fuel ratio to the stoichiometric air fuel ratio, rich spike processing is carried out (for example, see Patent Literature 1).